In this question we consider a variation on the Cournot model of competition between two firms called 1 and 2. Their strategies consist of simultaneous quantity choices. In terms of information each knows as much as the other. Collusion is ruled out. If qi is the quantity that firm i = 1,2 chooses, then, the price for firm 1s output will be p1(q1,q2) = 1 q1 0.5q2 and that of firm 2s output will be p2(q1,q2) = 1 q2 0.5q1. Firm i enjoysaconstantmarginalcostofci [0,1]. Assume4c1 c2 3and4c2 c1 3. 4. Each firms marginal cost of production is not a given but depends on how much each invests in R&D. If firm i does not invest in R&D, its constant marginal cost is ci = 0.5. In order to achieve a constant marginal cost of ci = 0, a firm must pay t, where t > 0 is a parameter. The essential feature of this expression is that the smaller the marginal cost, the higher the R&D costs. Suppose firms first, simultaneously choose their marginal costs and pay the corresponding R&D cost. Then, with the marginal costs they have chosen, they compete ala Cournot as in part (3). Determine the equilibrium values of c1 and c2 as a function of t..